The purpose of this study is to find the highest dose of the investigational drug SGN-CD19A that can be given safely in patients with B-cell acute lymphoblastic leukemia (B-ALL) or aggressive non-Hodgkin lymphoma that has not responded to standard therapy. Researchers will also assess the preliminary effectiveness of this drug against these cancers.

SGN-CD19A has two parts: one (an antibody) that attaches to a protein called CD19 on the surface of cancer cells, and another (an anticancer drug called monomethyl auristatin F) that kills the cancer. SGN-CD19A is given intravenously (by vein).